u_f , u, are these two the same?

sharonyue · September 16, 2013, 04:20

Hi guys,

Wonderful day!

While Im digging into fvc::reconstruct(), after lots of effort, I made a little progress, Now Im confusing that:
$\sum {{n_f}\left( {{S_f} \cdot u} \right)} = \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)}$

namely:

Is this rite? Only by this I can get the same equation as fvc::reconstruct().

Bernhard · September 16, 2013, 04:41

Can you add some linenumbers of relevant files? u and u_f are definitely not the same, as one would be a surface field and the other a volume field.

sharonyue · September 16, 2013, 04:46

Quote:

Originally Posted by Bernhard

Can you add some linenumbers of relevant files? u and u_f are definitely not the same, as one would be a surface field and the other a volume field.

I will make it more clear later, texting these equations in mathtype is time-consuming. Thank you very much. U help me alot...

sharonyue · September 16, 2013, 19:37

Sorry, so late!

$\begin{array}{l} \sum {{n_f}\left( {{S_f} \cdot u} \right) = } \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)} \\ \sum {\left[ {\left( {{n_F} \otimes {S_f}} \right) \cdot u} \right]} = \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} \left( {{S_f} \cdot {u_f}} \right)\\ \sum {\left[ {\left( {\frac{{{S_f}}}{{\left| {{S_f}} \right|}} \otimes {S_f}} \right) \cdot u} \right]} = \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} {\phi _f}\\ u = \underbrace {{{\left\{ {\sum {\left[ {\left( {\frac{{{S_f}}}{{\left| {{S_f}} \right|}} \otimes {S_f}} \right)} \right]} } \right\}}^{ - 1}} \cdot \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} {\phi _f}}_{weller's\;fvc::reconstruct()} \end{array}$

this might be clear. Any ideas?

sharonyue · September 22, 2013, 21:01

any ideas?

September 16, 2013, 04:20	u_f , u, are these two the same?	#1
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 838 Rep Power: 17	Hi guys, Wonderful day! While Im digging into fvc::reconstruct(), after lots of effort, I made a little progress, Now Im confusing that: $\sum {{n_f}\left( {{S_f} \cdot u} \right)} = \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)}$ namely: Is this rite? Only by this I can get the same equation as fvc::reconstruct().

September 16, 2013, 04:41		#2
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	Can you add some linenumbers of relevant files? u and u_f are definitely not the same, as one would be a surface field and the other a volume field.

September 16, 2013, 19:37		#4
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 838 Rep Power: 17	Sorry, so late! $\begin{array}{l} \sum {{n_f}\left( {{S_f} \cdot u} \right) = } \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)} \\ \sum {\left[ {\left( {{n_F} \otimes {S_f}} \right) \cdot u} \right]} = \sum {\frac{{{S_f}}}{{\left\| {{S_f}} \right\|}}} \left( {{S_f} \cdot {u_f}} \right)\\ \sum {\left[ {\left( {\frac{{{S_f}}}{{\left\| {{S_f}} \right\|}} \otimes {S_f}} \right) \cdot u} \right]} = \sum {\frac{{{S_f}}}{{\left\| {{S_f}} \right\|}}} {\phi _f}\\ u = \underbrace {{{\left\{ {\sum {\left[ {\left( {\frac{{{S_f}}}{{\left\| {{S_f}} \right\|}} \otimes {S_f}} \right)} \right]} } \right\}}^{ - 1}} \cdot \sum {\frac{{{S_f}}}{{\left\| {{S_f}} \right\|}}} {\phi _f}}_{weller's\;fvc::reconstruct()} \end{array}$ this might be clear. Any ideas?

September 22, 2013, 21:01		#5
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 838 Rep Power: 17	any ideas?